Comments on: Cut The Knot
http://www.metafilter.com/67078/Cut-The-Knot/
Comments on MetaFilter post Cut The KnotSat, 01 Dec 2007 23:52:38 -0800Sat, 01 Dec 2007 23:52:38 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Cut The Knot
http://www.metafilter.com/67078/Cut-The-Knot
<a href="http://www.cut-the-knot.org/content.shtml">Interactive mathematics miscellany and puzzles</a>, including <a href="http://www.cut-the-knot.org/pythagoras/index.shtml">75 proofs</a> of the Pythagorean Theorem, an <a href="http://www.cut-the-knot.org/ctk/index.shtml">interactive column</a> using Java applets, and <a href="http://www.cut-the-knot.org/pythagoras/tricky.shtml">eye-opening demonstrations</a>. (Actually, <a href="http://www.cut-the-knot.org/Curriculum/index.shtml">much more</a>.)post:www.metafilter.com,2007:site.67078Sat, 01 Dec 2007 23:52:10 -0800parudoxmathmathematicspuzzlesjavainteractivealgebrageometryprobabilityillusionsfractalsBy: parudox
http://www.metafilter.com/67078/Cut-The-Knot#1933043
I know it's been <a href="http://www.metafilter.com/30567/Cut-the-Knot">posted before</a>, but the site is pretty awesome, and I'm sure it's <a href="http://www.cut-the-knot.org/changes.shtml">gained</a> much content since then.comment:www.metafilter.com,2007:site.67078-1933043Sat, 01 Dec 2007 23:52:38 -0800parudoxBy: Upton O'Good
http://www.metafilter.com/67078/Cut-The-Knot#1933059
This is excellent. Thank you.comment:www.metafilter.com,2007:site.67078-1933059Sun, 02 Dec 2007 00:28:11 -0800Upton O'GoodBy: cogneuro
http://www.metafilter.com/67078/Cut-The-Knot#1933084
Great site that I hadn't know about, from someone who wants to enthusiastically share his deep love of math with others. I liked the dynamic versions of optical illusions (which have more to do with psychology than math) and the section on math and language (where he compares how mathematical laws were stated before and after the invention of relevant notation).
I don't think he gets very far toward understanding why people find math more formidable and less accessible than music and reading, though. It's an interesting question. The author emphasizes the beauty and elegance of math and clearly wants other people to be able to share in it. Yet few do (in the general population; maybe not among MeFites). Why?
One obvious point is that a person can engage reading and music at different levels that are enjoyable for a variety of reasons. Most people who listen to music don't know musical theory. You can read Us magazine or a technical article or Borges novels.
Getting to the point where you really appreciate the beauty, elegance, connectedness etc. of math seems to require a high level of expertise. The examples on that web site are not trivial math from what I've seen.
There's also the possibility that expertise in math takes a special kind of intelligence. Reading builds on basic capacities to see, hear, and use language. Not much special expertise there. At the simplest level, music enjoyment arises out of basic properties of hearing and motor control. nothing too specialized there. Math, however, seems to require specialized knowledge that only some people may be able to acquire because the underlying capacities vary greatly among individuals.
I don't pretend these are the answers but the web site brought them to mind.comment:www.metafilter.com,2007:site.67078-1933084Sun, 02 Dec 2007 02:12:39 -0800cogneuroBy: elpapacito
http://www.metafilter.com/67078/Cut-The-Knot#1933146
Ahhh sweet post, thanks !comment:www.metafilter.com,2007:site.67078-1933146Sun, 02 Dec 2007 06:27:01 -0800elpapacitoBy: Brian B.
http://www.metafilter.com/67078/Cut-The-Knot#1933180
Who knew that President J<a href="http://en.wikipedia.org/wiki/James_A._Garfield">ames Garfield</a> is credited with a <a href="http://www.geocities.com/CapeCanaveral/Launchpad/3740/garfield.html">proof for the Pythagorean theorem? </a> (See also proof 5 in the 75 proofs link.)comment:www.metafilter.com,2007:site.67078-1933180Sun, 02 Dec 2007 08:10:34 -0800Brian B.By: DU
http://www.metafilter.com/67078/Cut-The-Knot#1933215
Me.
(ObTwoNonConsecutiveProofs)comment:www.metafilter.com,2007:site.67078-1933215Sun, 02 Dec 2007 09:31:02 -0800DUBy: Opposite George
http://www.metafilter.com/67078/Cut-The-Knot#1933604
The first thing I checked when I saw the 75 proofs link was whether Pres. Garfield's proof made it (yay!) Had a prof show it to me years ago -- had to get independent confirmation that it really was Garfield's and not some elaborate hoax.
He came up with his proof while serving in the House of Representatives. Probably born in an inspired doodling session triggered by a boring committee meeting, if God has a sense of humor.comment:www.metafilter.com,2007:site.67078-1933604Sun, 02 Dec 2007 17:02:53 -0800Opposite GeorgeBy: fracturing
http://www.metafilter.com/67078/Cut-The-Knot#1934350
Can you imagine if our president now was able to do ANY proofs, much less a 75-step one? :)
I just hope that Pres. Garfield was working on that proof during non-vital issues! Yeep! Can you imagine mis-voting on a spending bill or something cuz you were finally getting close to a^2+b^2=c^2 ?!comment:www.metafilter.com,2007:site.67078-1934350Mon, 03 Dec 2007 09:31:48 -0800fracturingBy: parudox
http://www.metafilter.com/67078/Cut-The-Knot#1934463
Garfield's proof is by no means 75 steps — it's short and quite elegant, actually. (P.S. The links above are for clicking.)comment:www.metafilter.com,2007:site.67078-1934463Mon, 03 Dec 2007 10:56:58 -0800parudoxBy: phliar
http://www.metafilter.com/67078/Cut-The-Knot#1935068
Cogneuro: Keith Devlin makes a compelling argument in <a href="http://www.amazon.com/exec/obidos/ASIN/0465016197/metafilter-20/ref=nosim/">The Math Gene</a> that the quality in our brain that lets us do math is the <em>same</em> as that which lets us use and create language. Math ability is universal; "math phobia" is an attribute of <em>this</em> society.
It's an excellent book, I can't recommend it too highly.comment:www.metafilter.com,2007:site.67078-1935068Mon, 03 Dec 2007 20:45:19 -0800phliarBy: fracturing
http://www.metafilter.com/67078/Cut-The-Knot#1937958
D'oh! Apparently I shouldn't make fun of Bush when my reading comprehension skills were questionable. :)comment:www.metafilter.com,2007:site.67078-1937958Thu, 06 Dec 2007 08:13:44 -0800fracturing
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